1. The problem statement, all variables and given/known data A line of buckets numbered 0,1,2... extends indefinitely to the left with an elephant behind each bucket. Initially, all of the buckets are empty but then peanuts start falling into bucket 0 at a rate of one per second for 2^12 seconds. Whenever 5 peanuts accumulate in a bucket the elephant behind the bucket picks up all five, eats four, and places the remaining one in the bucket immediately to the left. When there are no more peanuts to be eaten, how many peanuts remain in each bucket?